An efficient dynamic optimization method for sequential identification of group-testable items

Abstract

Group testing with variable group sizes for incomplete identification has been proposed in the literature but remains an open problem because the available solution approaches cannot handle even relatively small problems. This article proposes a general two-stage model that uses stochastic dynamic programming at stage 2 for the optimal group sizes and non-linear programming at stage 1 for the optimal number of group-testable units. By identifying tight bounds on the optimal group size for each step at stage 2 and the optimal initial purchase quantity of the group-testable units at stage 1, an efficient solution approach is developed that dramatically reduces both the number of functional evaluations and the intermediate results/data that need to be stored and retrieved. With this approach, large-scale practical problems can be solved exactly within very reasonable computation time. This makes the practical implementation of the dynamic group-testing scheme possible in manufacturing and health care settings.

Keywords:

• Group testing
• incomplete identification
• variable sizes
• dynamic policy
• stopping rule
• bounds